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Results for “DISTRIBUTION FUNCTION”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Structural frequency functions for an impulsive, distributed forcing function

The response of a penetrator structure to a spatially distributed mechanical impulse with a magnitude approaching field test force levels (1-2 Mlb) were measured. The frequency response function calculated from the response to this unique forcing function is compared to frequency response functions calculated from response to point forces of about 2000 pounds. The results show that the strain gages installed on the penetrator case respond similiarly to a point, axial force and to a spatially distributed, axial force. This result suggests that the distributed axial force generated in a penetration event may be reconstructed as a point axial force when the penetrator behaves in linear manner.

Bateman, Vesta I.↗
NASA NTRS1992

Coherent structures in the universe and the adhesion model

An adhesion model is used to study the formation process of large-scale structures due to nonlinear gravitational growth of small initial fluctuations in the universe dominated by dark matter. The model is compared with 2D N-body simulations with initial power-law spectral indices n = -2, 0, +2, and various cutoffs. It is found that the adhesion model imitates the skeleton of the structure extremely well for the parameters of the initial spectra until the stage when the nonlinear scale reaches the correlation length R(phi) of the initial gravitational potential. The model explains the origin of large-scale coherent sructures, such as superpancakes and superfilaments, as a result of coherent motion of clumps due to large-scale inhomogeneities in the initial gravitational potential. It is found that clumps of mass identified in the N-body simulations correspond to several knots in the adhesion model, which influences the way of calculating the mass distribution function. The distribution functions of velocities and masses of clumps and areas of cells in the adhesion model satisfy self-similar scaling laws of the n = 2 model.

Kofman, Lev↗
NASA NTRS1978

One-dimensional inhomogeneous Vlasov equilibria

Bernstein, Greene, and Kruskal (1957) showed how, given the electrostatic potential as a function of position, the entire distribution function for ions, and the distribution function for untrapped electrons in a one-dimensional two-species Vlasov plasma, one could determine the distribution function for the trapped electrons as the solution of an Abel integral equation. This result is generalized by replacing the statements about the distribution functions with the specification of the velocity-space distribution functions of both species at a single position in the plasma. Limiting cases are shown to correspond to the earlier treatment, and the applicability of the theory to experiment is discussed.

Crownfield, F. R., Jr.↗
NASA NTRS1985

Integral functions of electron lateral distribution and their fluctuations in electron-photon cascades

Monte Carlo simulated lateral distribution functions for electrons of EPC developing in lead, at superhigh energies (.1-1 PeV) for depths t or = 60 c.u. delta t=1t. c.u. are presented. The higher moment characteristics, i.e., variation, asymmetry, excess, are presented along with analytical solutions for the same characteristics at fixed observation level calculated to theory approximations A and B by using numerical inversion of the Laplace transformation. The conclusion is made of a complex, usually non-Gaussian shape of the function of the particle number distribution within a circle of given radius at fixed depth.

Ivanenko, I. P.↗
NASA NTRS1972

The solution of the relaxation problem for the Boltzmann equation by the integral iteration method

The Boltzmann equation is considered in terms of the problem of relaxation of some initial distribution function which depends only on velocities, to Maxwell's distribution function. The Boltzmann equation is given for the relaxation problem in which the distribution function f(t, u, v) is time dependent and is also dependent on two other variables u and v (the velocities of rigid spherical molecules). An iteration process is discussed in which the velocity space u, v is subdivided into squares, the distribution function in each square being approximated by the second-order surface from the values of the distribution function at nine points. The set of all of these points forms a network of u, v values at the nodes of which the distribution function can be found.

Limar, Y. F.↗
NASA NTRS1988

Conditions for the validity of unmagnetized-plasma theory in describing weakly magnetized plasmas

The application of the unmagnetized-plasma theory to the derivation of the expression for the dielectric tensor for weakly magnetized plasmas is examined. The analysis of Baldwin et. al. (1969) is employed to determine the conditions under which the magnetic effects on the dielectric tensor of a plasma are small. The relation between wave and plasma parameters and the plasma distribution function is studied. Axisymmetric distribution functions in magnetized plasma are considered. The derived conditions are analyzed in terms of resonance ellipses of the cyclotron maser theory. Examples are presented in which the conditions are applied to a nonrelativistic Maxwellian distribution and the dispersion and instability of Langmuir and Bernstein waves in weakly magnetized plasma. The data reveal that the conditions under which the magnetic field can be completely neglected depend on the forms of the distribution function.

Robinson, P. A.↗
DOE OSTI2024

Stochastic Averaging of Radiative Transfer Coefficients for Relativistic Electrons

Abstract Synchrotron emissivities, absorptivities, and Faraday rotation and conversion coefficients are needed in modeling a variety of astrophysical sources, including Event Horizon Telescope (EHT) sources. We develop a method for estimating transfer coefficients that exploits their linear dependence on the electron distribution function, decomposing the distribution function into a sum of parts each of whose emissivity can be calculated easily. We refer to this procedure as stochastic averaging and apply it in two contexts. First, we use it to estimate the emissivity of an isotropicκdistribution function with a high-energy cutoff. The resulting coefficients can be evaluated efficiently enough to be used directly in ray-tracing calculations, and we provide an example calculation. Second, we use stochastic averaging to assess the effect of subgrid turbulence on the volume-averaged emissivity and along the way provide a prescription for a turbulent emissivity. We find that for parameters appropriate to EHT sources turbulence reduces the emissivity slightly. In the infrared, turbulence can dramatically increase the emissivity.

Astronomy & Astrophysics↗
NASA NTRS1966

X-ray analysis of fatigue damage in copper

A Warren-Averbach x-ray line profile analysis was applied to, broadened x-ray diffraction peaks from copper deformed in fatigue. The copper specimens were fatigued by four point bending at various strain amplitudes, and measurements were made at various fractions of the total fatigue life. The analysis results in an estimation of 1) an average coherently diffracting domain size in a direction normal to the diffracting planes; and 2) a strain distribution function. The strain distribution function is in terms of the root mean square strain, <ϵ^(2)> where ϵ is averaged over a given distance at all points in the diffracting crystals. This rms strain is expressed as a function of averaging distance for a direction normal to the diffracting planes. The rms strains were found to be a function of the fatigue strain amplitude level, increasing with amplitude and reaching a maximum limiting value during the first 2% of the fatigue life. The strains were normally larger in the 4lO0 direction compared to the <111> direction and the absolute values were quite small. These results may be explained by assuming the dislocations are present in the form of dipoles because the lattice strain around a dipole is much less than around single dislocations. Conclusions arrived at in this analysis are in agreement with current theories of fatigue damage in metals. The result that maximum hardening is achieved during the initial few percent of the fatigue life is confirmed by many other investigators using entirely different analytical techniques. It is felt that the structure of the material is changing during this initial hardening stage to an eventual steady state characteristic of the testing conditions. A unique substructure is developed which thereafter persists, and the remainder of the fatigue test is taken up by crack propagation through this substructure until ultimate failure occurs by fracture. The formation of this steady state structure is dependent on the maximum fatigue strain amplitude and on the frequency and temperature of cycling for a particular material.

COPPER↗
NASA NTRSDate not supplied

Assessing the Viability of Using GEOS-Forecast Product for Landslides Forecasting: A Step Toward Early Warning System

Landslides across the globe are mostly triggered by extreme rainfall events affecting infrastructure, transportation and livelihoods. The risks are rarely quantified due to lack of data, analytical skills and limited modeling techniques. Knowledge of local to global scale landslide risks provides communities and national agencies the ability to adapt disaster management practices to mitigate and recover from these hazards. In order to minimize the risks and improve characterization of community resilience to landslides, it is vital to have reliable information about the factors triggering landslides such as rainfall, well ahead in time. Forecasting potential landslide activity and impacts can be achieved through reliable precipitation forecast models. However, it is challenging because of the temporal and spatial variability of precipitation, an important factor in triggering landslides. Evaluation of the precipitation field, associated errors, and sampling uncertainties is integral for development of efficient and reliable landslide forecasting and early warning system. This study develops a methodology to assess the viability of using a precipitation field provided by a global model and its potential integration in the landslide forecasting system. The study focuses on the comparison between the IMERG (Integrated Multi-satellitE Retrievals for Global Precipitation Mission) and GEOS (NASA Goddard Earth Observing System)-Forecast product over contiguous United States (CONUS). GEOS model assimilates new observations every 6 hours, at 00, 06, 12, and 18 UTC. The framework is tested on the GEOS-Forecast Model initialized at 00 UTC using daily IMERG early product as reference using both categorical and continuous statistics. The categorical statistics includes the probability of detection (POD), success ratio (SR), critical success index (CSI), and the hit bias. Continuous statistics such as correlation, normalized standard deviation, and root-mean-square error are also evaluated. Overall, GEOS-Forecast precipitation field over the analysis period (~1 year) show underestimation with respect to IMERG early for the daily accumulated rainfall. However, the probability distribution function and cumulative distribution function of both show similar patterns. In terms of correlations, POD, SR, CSI, hit bias, the performance varies with respect to the rainfall threshold used.

Sana Khan↗
NASA NTRS2018

Behavior of Triple Langmuir Probes in Non-Equilibrium Plasmas

The triple Langmuir probe is an electrostatic probe in which three probe tips collect current when inserted into a plasma. The triple probe differs from a simple single Langmuir probe in the nature of the voltage applied to the probe tips. In the single probe, a swept voltage is applied to the probe tip to acquire a waveform showing the collected current as a function of applied voltage (I-V curve). In a triple probe three probe tips are electrically coupled to each other with constant voltages applied between each of the tips. The voltages are selected such that they would represent three points on the single Langmuir probe I-V curve. Elimination of the voltage sweep makes it possible to measure time-varying plasma properties in transient plasmas. Under the assumption of a Maxwellian plasma, one can determine the time-varying plasma temperature T(sub e)(t) and number density n(sub e)(t) from the applied voltage levels and the time-histories of the collected currents. In the present paper we examine the theory of triple probe operation, specifically focusing on the assumption of a Maxwellian plasma. Triple probe measurements have been widely employed for a number of pulsed and timevarying plasmas, including pulsed plasma thrusters (PPTs), dense plasma focus devices, plasma flows, and fusion experiments. While the equilibrium assumption may be justified for some applications, it is unlikely that it is fully justifiable for all pulsed and time-varying plasmas or for all times during the pulse of a plasma device. To examine a simple non-equilibrium plasma case, we return to basic governing equations of probe current collection and compute the current to the probes for a distribution function consisting of two Maxwellian distributions with different temperatures (the two-temperature Maxwellian). A variation of this method is also employed, where one of the Maxwellians is offset from zero (in velocity space) to add a suprathermal beam of electrons to the tail of the main Maxwellian distribution (the bump-on-the-tail distribution function). For a range of parameters in these non-Maxwellian distributions, we compute the current collection to the probes. We compare the distribution function that was assumed a priori with the distribution function one would infer when applying standard triple probe theory to analyze the collected currents. For the assumed class of non-Maxwellian distribution functions this serves to illustrate the effect a non-Maxwellian plasma would have on results interpreted using the equilibrium triple probe current collection theory, allowing us to state the magnitudes of these deviations as a function of the assumed distribution function properties.

Polzin, Kurt A.↗
NASA NTRS1982

Some axisymmetric self-similar galaxy models

Distribution functions are presented for some axisymmetric self-similar galaxy models with flat rotation curves. In particular, we record velocity distribution functions for the logarithmic potentials studied by Richstone. These distribution functions depend on two integrals only. Other distribution functions (possibly involving more or other integrals) associated with the same mass model differ only by an additive function that integrates over velocities to yield zero density everywhere. However, a given distribution function can be associated with different mass models.

Miller, R. H.↗
NASA NTRS1992

Accelerated cometary ions observed downstream of the Comet Halley bow shock

Results are presented of fluxes of energetic ions with energies exceeding 100 keV that were detected upstream of the bow shock of Comet Halley by the Tuende instrument on board the VEGA 1 spacecraft. Downstream of the shock, ion fluxes in the energy range 100 to 180 keV were observed. The measured ion fluxes were transformed into distribution functions in the solar wind frame using a variety of assumptions concerning the energy dependence of the distribution function and the identity of the ion species. The derived distribution function upstream of the shock falls off steeply with energy between 100 and 150 keV, with an effective temperature of about 7 keV or spectral index of about -15. The distribution function increases with decreasing cometocentric distance, on average, reaching a maximum at the bow shock. The measured distribution functions are compared with those obtained by similar instruments on Giotto and ICE as well as with the predictions of several theoretical models that employ different acceleration mechanisms.

Kecskemety, K.↗
NASA NTRS2006

Representation of the Geosynchronous Plasma Environment in Spacecraft Charging Calculations

Historically, our ability to predict and postdict spacecraft surface charging has been limited by the characterization of the plasma environment. One difficulty lies in the common practice of fitting the plasma data to a Maxwellian or Double Maxwellian distribution function, which may not represent the data well for charging purposes. We use electron and ion flux spectra measured by the Los Alamos National Laboratory (LANL) Magnetospheric Plasma Analyzer (MPA) to examine how the use of different spectral representations of the charged particle environment in computations of spacecraft potentials during magnetospheric substorms affects the accuracy of the results. We calculate the spacecraft potential using both the measured fluxes and several different fits to these fluxes. These measured fluxes have been corrected for the difference between the measured and calculated potential. The potential computed using the measured fluxes and the best available material properties of graphite carbon, with a secondary electron escape fraction of 81%, is within a factor of three of the measured potential for 87% of the data. Potentials calculated using a Kappa function fit to the incident electron flux distribution function and a Maxwellian function fit to the incident ion flux distribution function agree with measured potentials nearly as well as do potentials calculated using the measured fluxes. Alternative spectral representations gave less accurate estimates of potential. The use of all the components of the net flux, along with spacecraft specific average material properties, gives a better estimate of the spacecraft potential than the high energy flux alone.

Davis, V. A.↗